Реферат: The Boussinesq problem describing indentation of a rigid punch of arbitrary shape into a deformable solid body is studied within the context of a linear viscoelastic model. Due to the presence of a non-local integral constraint prescribing the total contact force, the unilateral indentation problem is formulated in the general form as a quasi-variational inequality with unknown indentation depth, and the Lagrange multiplier approach is applied to establish its well-posedness. The linear viscoelastic model that is considered assumes that the linearized strain is expressed by a material response function of the stress involving a Volterra convolution operator, thus the constitutive relation is not invertible. Since viscoelastic indentation problems may not be solvable in general, under the assumption of monotonically non-increasing contact area, the solution for linear viscoelasticity is constructed using the convolution for an increment of solutions from linearized elasticity. For the axisymmetric indentation of the viscoelastic half-space by a cone, based on the Papkovich-Neuber representation and Fourier-Bessel transform, a closed form analytical solution is constructed, which describes indentation testing within the holding-unloading phase.

Библиографическая ссылка: Itou H. , Kovtunenko V.A. , Rajagopal K.R.
Lagrange multiplier approach to unilateral indentation problems: Well-posedness and application to linearized viscoelasticity with non-invertible constitutive response
Mathematical Models and Methods in Applied Sciences. 2021. V.31. N03. P.649-674. DOI: 10.1142/s0218202521500159 WOS Scopus РИНЦ OpenAlex

Идентификаторы БД:

Web of science:	WOS:000651438800006
Scopus:	2-s2.0-85101743497
РИНЦ:	46757568
OpenAlex:	W3134088252

Цитирование в БД:

БД	Цитирований
Scopus	7
OpenAlex	8
РИНЦ	8
Web of science	8

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